I am working on an inverse problem of parameter
identification of diffusion equations of the following form

d u(x,t)/ dt = div(D(x)grad(u(x,t)) - m(x)u(x,t) + s(x,t) .

D(x) and m(x) are the unknown parameter functions.
s(x,t) and the flux in normal direction of u on the boundary is known
for different s(x,t), in general a delta-function in space and time.
The iterative inverse procedure is based on the repeated solution of
the forward problem with known parameter functions. I am looking for
a 3D solver for the diffusion equation, commercial or scientific
software possibly with source code. Any suggestions would be appriciated.
Thanks.

This is a problem of identifying the non-efficient vectors
given a set of potentially efficient/non-dominated vectors.
A typical application for this is multi objective optimization.

Consider a finite set S of vectors in R^m,
S = { v_1, v_2, ... , v_n }
A vector v_k in S is said to be efficient (or non-dominated or
Pareto-minimal) in S iff there does not exist j in {1,2,...,n}
such that
v_j(i) <= v_k(i) , for all i in {1,2,...,m}
[v_j(i) indicates the ith component of v_j]
and
v_j(i) < v_k(i) for some i in {1,2,...,m}

The problem is to weed out the non-efficient vectors from S
computationally. Naively, this can be done in O(mn) comparisons.
Is there a smarter way leading to a better complexity result ?

In the March 31 issue (13/96) of NA Digest we announced the SciTools'96
workshop to take place in Oslo, Norway this September. Since the
announcement was made, we have been contacted by the international
publisher Birkhauser concerning the possibility of publishing a book
based on carefully selected contributions to the workshop. We feel that
this information is important and it should therefore be communicated to
our potential contributors. For further details, see the workshop web
pages at http://www.oslo.sintef.no/SciTools96/.

The goal of the 5th International Meshing Roundtable is to bring
together researchers and developers from industry, academia, and
government labs for the exchange of technical information related to
automatic mesh generation. The Roundtable will include an invited
panel of experts discussing topics suggested by the attendees. There
will be numerous opportunities for informal dialog between attendees.
Accepted papers will be published (by Sandia National Laboratories) in
a proceedings, and made available on the WWW if possible.

TRAVEL FUNDS available for
WOMEN Graduate Students and Recent Ph.D.s
in the Mathematical Sciences

Julia Robinson Celebration of Women in Mathematics
to be held
July 1-3, 1996
at MSRI, Berkeley, California

supported by the National Security Agency, the
Mathematical Sciences Research Institute and the
Association for Women in Mathematics

The celebration of the 25th anniversary of the Association of Women
in Mathematics (AWM) will culminate in the Julia Robinson
Celebration of Women in Mathematics conference. All mathematicians
are invited to attend the conference. The goals of the celebration
are:

* to showcase the recent achievements of women in mathematics;
* to facilitate networking among women in various fields of
mathematics;
* to provide role models and offer mentoring for beginning women
mathematicians;
* outreach to area teachers and students.

The Celebration will be a two and a half day conference to be held
July 1-3, 1996, at the Mathematical Sciences Research Institute
(MSRI) in Berkeley, California. Details of the program can be found
in the MSRI homepage: http://www.msri.org/

Approximately 40 grants to attend the conference will be available to
women in the mathematical sciences. In awarding these grants, preference
will be given to women graduate students and recent Ph.D.s. Applicants
should include a cover letter, an outline of their research (maximum two
double-spaced pages) and a curriculum vita. Graduate student applicants
should also include a letter of recommendation from their advisors. All
non-U.S. citizen applicants must have a current U.S. address.

Send FIVE complete copies of the application materials (including
the cover letter) to:

Second Announcement and Final Call for Papers
SIXTH CONFERENCE OF THE
INTERNATIONAL LINEAR ALGEBRA SOCIETY

August 14-17, 1996, Chemnitz (GERMANY)

PURPOSE
To bring together researchers and educators in all fields of Linear Algebra
from Numerical Linear Algebra to Algebra, pure and applied, allowing a broad
exchange of ideas and discussion of recent developments in these areas.
Special emphasis: Numerical Linear Algebra, Computational Algebra.

CALL FOR PAPERS
Contributed papers from all areas of linear algebra and applications are
solicited. Papers fitting within the scope of the conference will be
accepted, subject to unavoidable limitations of space and time. Selected
papers will be scheduled as 15(+5)-minute presentations in concurrent
sessions.
Two copies of an extended one-page abstract should be submitted by May 1,
1996, to

Electronic submissions are encouraged. Abstracts should mention all authors
and their affiliations. Please also provide the postal and e-mail address
(or fax number) of the corresponding author to facilitate correspondence.
The abstracts will be collected in a book of abstracts distributed at the
conference. A selection of papers will also be collected in the conference
proceedings but these have to be submitted separately.

Sixth Viennese Workshop on
Optimal Control, Dynamic Games and Nonlinear Dynamics
Theory and Applications in Economics and OR/MS

Vienna , May 21-23, 1997

After five successful workshops on various similar topics the Sixth Viennese
workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics will again
bring together researchers interested in the application of nonlinear methods
in economics, operations research and management science. Topics of interest
are optimal control theory, dynamic programming, differential games,
evolutionary games, learning, economic modelling, chaos theory, complex
systems and related fields. Theoretical contributions to one of these fields
which are relevant to problems from economics or OR/MS are especially welcome
but also applied modelling will be covered.

The attendance will be limited, and due to the lack of sufficient financial
support by private and public organizations a registration fee of ATS 1500.-
(approx. US$150.-) will be charged. In addition to the scientific program an
extensive social program will be organized.

Tool Command Language (Tcl)/ Tool Kit (Tk) is a GUI development tool which
has been increasingly adapted in a variety of applications. This two day course
is aimed at programmers and project managers with particular interest in the
development of inexpensive but effective GUIs for their applications.

What has happened in Numerical Analysis during the last 10 years, and
what are the most interesting future developments in the field? These
questions were the topics in the conference 'State of the art in Numerical
Analysis' held April 1-4 in York, England. The conference has been
arranged every tenth year since 1966 by IMA (The Institute of Mathematics
and its Applications), and this year it gathered 112 mathematicians from
about 16 countries. Gene Golub asked me to summarize the conference for
the NA-Net readers:

The conference centered around the central themes in numerical analysis:

And in addition there was a session on new applications. I will here give
a brief personal summary of the various topics, which of course to some
extent is colored by my own personal interests. All the talks will appear in
the conference proceedings, published by IMA. Judged from the quality of
the talks, this will be a very valuable reference source.

Linear Algebra:

Talks were given by Nick Higham (dense linear algebra), Iain Duff (sparse
direct methods), Gene Golub (iterative methods for linear systems) and
Henk van der Vorst (sparse eigenproblems). The main developments in dense
linear algebra during the last 10 years has been centered around all the work
with the LAPACK project for dense linear algebra. Parallel computers have been
around only for about a decade, so most of the work on parallel linear
algebra is done in this period. This is now seen through the organization
of algorithms around block formulations via the BLAS 2 and 3 routines.
Interestingly, also sequential computers gain speed by this organization.
Also in sparse computations, much of the activity has been inspired by
parallel computers. For iterative methods, the main contributions during
the last decade is perhaps the development of Krylov subspace techniques
for unsymmetric systems (GMRES, CGS, Bi-CGSTAB, QMR). And in eigenproblems
there have been a significant development of Lanczos and Arnoldi type
methods. Some old methods have gained new significance (Jacobi) and some
new ideas have been introduced due to parallel computers (divide and
conquer algorithms). Even some new basal mathematical tools have gained
significant importance (pseudospectra).

Where are we going now? It seems as parallelism per se is not a topic of
major popularity, but it will of course remain constantly in our heads when
we contemplate over new algorithms. Since the 'black box' software
packages in linear algebra is now so excellent, much work in the future will be
centered around exploiting structures which arise in various application
areas. This was pointed out by Gene, who said that he 'just late in life'
realized the importance of exploiting all the information which comes from
knowing the structure of the underlying problems. A lot of this
information is lost if we regard our problems as being 'purely' linear
algebra.

Ordinary differential equations:

In this area, the need for alternatives to the 'black box' software was
even more emphasized than in linear algebra. All the three speakers; Chus
Sanz-Serna (geometric integrators), Andrew Stuart (dynamical systems) and Arieh
Iserles (beyond the classical theory of ODEs), pointed out that there is a
major need for understanding how to conserve various properties of equations
that are essential mathematically, and which has not been given enough
consideration numerically. Chus summarized the work done during the last 10
years on preserving symplecticity and Andrew Stuart talked about recovering
the correct asymptotic properties of dissipative dynamical systems (limit
sets and attractors). Here the classical notion of measuring quality
by the global error is not relevant. Ariehs talk summarized the work done
on delay differential equations and differential algebraic systems during the
last decade. He pointed out some areas of significant current research,
where we may gain major insight in the next decade. This includes the work
currently undertaken to understand the integration of equations where the
solution is known to sit on a specific manifold or on a Lie group. In the
discussion someone pointed out that "Whereas one 20 years ago didn't need
to know much about differential equations to work with numerical solutions
of them, this is no longer the case".

Integral equations:

Two talks were given about integral equations; Christopher Baker (Volterra
functional and integral equations), Kendall Atkinson (Boundary integral
equations). Also in these areas the last decade has been very fruitful. For
boundary integral equations much of the understanding of the numerical
analysis of corner singularities have been gained in this period. For me
as an outside viewer in this field, the most fascinating developments have
perhaps been the various fast algorithms for solving the dense matrix
problems arising in these fields. (Fast multipole algorithms and algorithms
based on wavelet compression and multiresolution analysis). Now the
solution techniques for these dense linear algebra problems have become so fast
that it is important not to form the coefficient matrix explicitly. (The
complexity of solving the linear systems is smaller than the complexity of
assembling the coefficient matrix!)

Approximation:

Talks were given by Alistair Watson (emphasis on the univariate case),
Mike Powell (multivariate interpolation), David Broomhead (neural net
approximations). The most important development in approximation has
probably been the field of wavelets, briefly summarized in Watsons talk.

Optimization:

Three talks in this field: Jorge Nochedal (unconstrained optimization),
David Shanno (interior point methods), Nick Gould (nonlinear constraints).
There has been a tremendous amount of work on interior point methods this
decade, and Shanno referred to large industrial optimization problems where
interior point methods beat simplex by a factor 50 in speed.

There were two talks on applications; Frank Natterer (Tomography) and
Jean-Michel Morel (nonlinear filtering and PDEs). Morels talk about the
connection between filtering techniques in computer vision and partial
differential evolution equations was highly inspiring. The idea is to
classify various families of discrete image filters via the PDEs they
approximate. In some sense, the work in this field resembles the early work
on statistical mechanics/ transport theory/ continuum mechanics in the
last century. This is an area in its infancy, where the basic
understanding of the processes involved is being developed in the language
of PDEs.

Concluding remarks:

It is hard to summarize all the developments that has been going on in
numerical analysis during the last decade. It has been an immensely
fruitful period, and the subject is truly alive and developing.

It is also a pleasure to remark that the numerical analysis community consists
of a bunch of cheerful people, and that the friendly spirit of the 'late
hours' is also a part of the 'State of the Art' in our field. This was
evident in the hilarious dinner speech by John C. Mason. Thanks to the
organizing committee chaired by Alistair Watson, and to Pamela Bye for
arranging all the practical details.

Info is also found at:
http://www.amtp.cam.ac.uk/user/na/SotANA/SotANA.html

The Optimization Project of the Center for Research on Parallel Computation
has a postdoctoral position in applications and algorithm development for
large scale numerical nonlinear programming. This position will be under
the direction of Professor John Dennis and Professor Matthias Heinkenschloss
and will be a research appointment in the Department of Computational &
Applied Mathematics.

DUTIES: Conduct independent and joint research in computational
optimization problems rooted in engineering. Specific areas of activity
include optimization software development, development of research
directions, interface with application scientists and engineers,
supervision of graduate and undergraduate research assistant, including
research seminar organization.

QUALIFICATIONS: Applicant must have excellent communication skills and an
ability to work with specialists in varied fields. Applicant must have
demonstrated interest and expertise in at least two of the following:
Algorithm development for nonlinear programming, numerical software
development, nonlinear programming approaches to engineering design or
parameter identification. Ph.D. or equivalent. Applicant's record of
publication will be considered.

Sandia National Laboratories invites outstanding candidates to apply
for a postdoctoral position in computational sciences. Postdoctoral
positions at Sandia provide an exceptional opportunity for innovative
research in scientific computing on advanced architectures and are
intended to promote the transfer of technology from the laboratory
research environment to industry and academia through the advanced
training of new computational scientists. Candidates should have a
Ph.D. or the equivalent in applied mathematics, computer science, or a
related field, and have a strong interest in computational modeling
research.

Sandia has strong research programs in scientific and parallel
computing and computational mathematics. We seek a candidate with a
research agenda to augment these programs in addition to a strong
interest in the development of state-of-the-art methods for solving
computational science problems. Sandia supports an excellent
computational environment that includes high-performance scientific
workstations and access to state-of-the-art parallel computers.

The postdoctoral position can be for periods of one, two, or three
years. Applications should be addressed to: Sandia National
Laboratories, attn: Anna Isham, Mail Stop 9111, HR Department,
8522-CA0011, P.O. Box 969, Livermore, CA 94551, and must include a
resume' and the names and addresses of three references.

UNIVERSITY OF NEWCASTLE UPON TYNE
DEPARTMENT OF ENGINEERING MATHEMATICS
RESEARCH ASSOCIATE

Theoretical study of two-phase gas-solid and gas-liquid flow.

This is a new three year EPSRC funded post in the area of turbulent two-phase
flow modelling. The research will involve the development and analysis of a
variety of mathematical models using both two-fluid and kinetic approaches,
and will contribute to on-going studies in this area within the Department.

Candidates should have a background in theoretical fluid dynamics and, ideally,
should have some knowledge of multi-phase systems. Experience in computer
programming and a knowledge of numerical methods applied to fluid dynamics
will also be an advantage.

Starting salary will be up to GBP16,628 pa on the Grade 1A scale
(GBP14,317 - GBP21,519 pa) according to qualifications and experience.

For information about the Department, see WWW URL http://www.ncl.ac.uk/~nengm/

ABB is a world-wide leader in power generation and distribution, industrial
automation, and mass transportation. In our Swiss Research Center near Zurich,
approximately 200 scientists and engineers are working on the basics of new
products for ABB. We have research projects in the areas of combustion
engineering, aerodynamics, environmental technology, materials science,
measurement techniques, and computer science.

Within our Computer Engineering Department, we have an immediate opening for a
permanent position as a

Scientific Computing Expert

The candidate should have a broad background in scientific computing. He or she
should be able to analyse practices in computational environments, identify
problems and find solutions, and should have experience in most of the
following levels of scientific computing:
- mathematical modeling
- numerical analysis
- parallel computing
- high-performance computing environments
- commercial simulation software
- UNIX system tuning
- computer networks

Communicative skills are essential, since the candidate will often have to
interface between scientists, engineers, and managers in very different fields,
advise them on improvements, and articulate ideas in their own terminology.
The position requires the willingness to learn German.

Interested applicants should submit a curriculum vitae by e-mail (ASCII or
PostScript) to <Claude.Pommerell@chcrc.abb.ch>, or to
Claude Pommerell
ABB Corporate Research
CH-5405 Baden-Daettwil
Switzerland

The Marquette University Department of Mathematics, Statistics,
and Computer Science has openings for two Industrial-Based
Graduate Research Assistantships in industrial and applied
mathematics. Students will pursue a Master of Science degree
while working closely with industrial sponsors Johnson Controls
and SC Johnson Wax. One assistantship requires skills in
operations research, the other in statistics and database
design.

Number of openings: two.
Duration: June 3 or August 15, 1996, through December, 1997.
Annual stipend: $12,000 + 18 tuition credits per year.
Deadline: All applications received by May 6 will be considered. If
no suitable candidates are found, applications will be welcomed,
and the positions will be filled by the first suitable applicant.

The NSF funding requires students to be citizens of the USA
or lawfully admitted permanent resident aliens.

An on-site interview at the applicant's expense will be required.

Students from groups traditionally underrepresented in the field
are especially sought.